Prep the ingredients per the instructions above.
Make the tzatziki: add all ingredients to a bowl and mix until combined. Season with salt and pepper to taste. Set aside in the refrigerator.
Drain the chickpeas well and place them on a paper towel to remove the remaining exterior moisture. Transfer drained chickpeas, red onion, garlic, cumin, lemon juice, paprika powder, parsley, salt, and black pepper to a food processor and pulse until roughly mashed. Stop the processor as needed to scrape down the sides of the bowl. You should achieve a paste-like consistency, but it doesn't need to be perfectly smooth – the mixture should remain slightly chunky.
Spoon the mixture into a large bowl, add the flour, baking powder, and sesame seeds, and stir until well combined. If the mixture is too moist or sticky at this stage, add a little bit more flour, until the mixture holds together. Then cover with plastic wrap and allow to rest in the refrigerator for 20 minutes.
Heat the oil in a large saucepan over medium heat, until the oil is hot (350 °F / 176°C). Fry the balls in batches, without crowding, until nicely browned, turning as necessary (about 2-3 minutes), and set aside on paper towels to drain.
Spread the wrap with tzatziki sauce. Layer with lettuce, falafel balls, onion, tomatoes, and feta. Fold in the ends and roll up tightly.
Cut in half and serve with hummus, pita chips, and lemonade.